how do you catch mew in pokemon emerald- any other helpful hints for rare pokemon?

Answer 1

I don't know on mew (i have sapphire) but if nest ball is in emerald, the easiest way is to use a swellow w/
1. red hp
2. endeavor
3. high speed
Put it together and: Use a swellow's (with hp in the red zone)
endeavor to get the pokemon's health down, then use a nest ball/ultra ball.

Answer 2

I think Mew's on Faraway Island, but you need to go to a Nintendo event. If all else fails, cheat.